Are self-employed persons eligible to use DBS Multiplier Account to log the money income to fulfil the criteria on salary crediting?

If your relatives are able to credit it in as SALARY, then yes.
If they just deposit the money in every month, it won’t fulfil the criteria of salary crediting

Extracted from DBS website,
Salary must be credited via GIRO, with transaction reference codes 'SAL' or 'PAY'.
This is reflected as either 'GIRO SALARY' or 'SALARY' in the main transaction description in your Statement of Account

You might want to look at other alternatives..
1. POSB SAYE- 2% if they bank in fixed amount every month for 2 years and do not touch the amount
2. UOB One- at least $500 spend on credit card (1.5%) and higher interest if you pay 3 bills by giro from the account
3. CIMB FastSaver -1%

Hope this helps:)